Recent content by ryan8888

Okay 1 final question. When I go to determine my roots what is the best way to handle the 2m^2? Is it the same as saying two numbers that multiply to -2 and add to -1. So my roots are m = 2 and m = -1? And I agree the y = x^m method is significantly easier to deal with! Thanks

Okay thanks. I didn't realize that you couldn't just simply utilize that formula for the characteristic equation. So I took y = xm and found its derivatives: y' = mxm-1 y" = m(m-1)xm-2 Substituting them into my original ODE and simplifying I obtain the following characteristic...

Homework Statement Solve: 2x2y" + xy' - y = 3x4 Homework Equations The Attempt at a Solution I know this is a Euler Cauchy solution because of the x2 before the y" in the ODE. I try to solve the characteristic equation m2 +(a-1)m + b = 0 I get 2m2 + (1-1)m - 1 =0 or 2m2 -...

Okay I see what you hac done there. I was browsing around the internet because I'm not familiar with variation of parameters and found the following: w = \left|\begin{array}{cc}y1a & y2 \\ y'1 & y'2\end{array}\right| which I solved to get x^2 The next step was to solve for w1 and w2...

Homework Statement Find the General Solution of x^2y" - 2xy' +2y = x^4e^x Homework Equations The Attempt at a Solution I just recently began learning about the Euler-Cauchy Equation and have been able to follow it until I hit the part for the Complementary Equation. I'm having a...

Awsome. Thanks for the help. I figured that the first portion of the question the f(x,y,z) had nothing do do with determing the equation of the plane. I came up with 3x - 2y - 2z = 9 for the equation of the plane that is tangent to g(x,y,z). I do have another question for part 2. I have taken...

Given: let f (x,y,z) = x2 + y2 + z2 = 2y - 3x and g(x,y,z) = 3x + y2 - z2 A. Find an equation for the tangent plane for the surface g(x,y,z) = 9 at the point (3, -1, 1) B. Find the line tangent to the intersection of the surfaces f(x,y,z) = 0 and g(x,y,z) =9 at the point (3,-1,1) A. I...

I can't believe I didn't catch the dividing out the common! THanks guys I got it now!

Please forgive me but I'm not following what you are saying here. I just don't see how 6x2 = y2 = 3z2 = t fits into the equation for the constraint.

1. Problem Statement: Use Lagrange multipliers to find the volume of the largest box with faces parallel to the coordinate system that can be inscribed in the ellipsoid: 6x2 + y2 + 3z2 = 2 2. Homework Equations : f(x,y,z) = \lambdag(x,y,z) 3. Attempt at a solution f(x,y,z) is the...

Never mind! I just realized that ln x^r = r ln x! That answers that question! Thanks for you help Ryan

Thanks again Mark. I just havn't come across that one to this point! But it is very helpful. I have one more unrelated one for you. I have to integrate 2/x. Now I come up with 2 * ln(x) but in my textbook example it shows the solution as ex2, so the answer would be x2. Am I missing something...

This is just what I was looking for. I didn't have that particular integral in my list of variations, do you happen to have a list of some of these less seen integrals of trig functions? Thanks for all of your help!

Hi all, I am trying to work out the following: cos2(t)sin(t)y' = -cos3(t)y + 1 I've moved put the equation into the standard form and determined that my integrating factor is the integral of cos(t)/sin(t) or the integral of cot(t). This gives me elnsinu +c or sin(t). I multiple both...

Okay, I was fairly certain that I had to use the derivatives of the yp solution since I have worked other examples and that is the technique that I used. So I have: yp = Ax3 + Bx2 + Cx + D y'p = 3Ax2 + 2Bx + C y"p = 6Ax + 2B Plugging them back into the Original ODE: (6Ax + 2B) +...